In sentences like “Man, that’s good,” or “Oh man... what are you gonna do?” how would you translate the use of “man”?
note: not the form of address, just a similar expression to “Oh no” or “Dang/Wow” or something like that
About man in "Man, that's good.", I don't think there's a word to translate it, and depending on the context it might get lost in translation.
For two people in a jacuzzi, I'd say
Qu'est-ce qu'on est bien !
But if you're tasting food or a drink, I'd say one of those
Hmm, c'est super bon !/C'est vraiment très bon !
Qu'est-ce que c'est bon !
which is even stronger. Qu'est-ce que can also intesify negative things like :
Qu'est-ce qu'il fait chaud ! (Man, it's so hot!)
For something annoying you can use sérieux ? or sérieusement ?. Like in "Man, you forgot your keys again? It's the third time this week!", even in English you can use seriously or are you kidding me?.
And I can't think of anything (yet) for something sad, like the "Oh man, I'm sorry." when you hear a bad news. I'd think you'd just omit it.
As an interjection (as opposed to an apostrophe, which @Greg covered), there are many terms which vary significantly between places, socio-cultural settings, etc.
Old-fashioned and/or local :
pardi ! (Man, slow down!)
Mazette, tu en as mis du temps ! (Man, what took you so long?)
Mince alors, c'est un super exemple ! (Man, that's one good example!) (works with both good and bad denotation)
Aïe, la voiture est encore en panne ! (Man, the car is broken again!) (only works with bad denotation)
Eh ben, ça faisait un bail ! (Man, it's been ages!)
Familiar, up-to-date :
Sérieux, j'en peux plus ! (Oh man, I can't take it anymore!)
Mon gars, t'as vu les infos ce matin ? (Man, did you watch the news this morning?) (not an address but an interjection in its own right, just like Man)
From a Quebec perspective, the anglicism “Oh boy!” is quite common. Though such integral loans from English are heavily frowned upon by many, and chased down like vermin by language institutions in place in the province, this one is still alive and well in familiar speech in 2019.
The fact boy is a masculine term is a bit blurred by the fact it is not a French word, but a basic knowledge of English has been common for centuries in Quebec’s population, so its masculinity is not a very big secret. However, this masculinity, though not secret, has also been masked away one layer deeper by the fact it has more or less become a set expression, like the “Man!” of the question. So there is no problem for one to say it to a woman, and women together without men around can still use it quite naturally and without any sense of ridicule.
There are plenty of interjections that can match, depending on the context.
Some will be close to the English "man", being directed at a male interlocutor that you want to take as some sort of "witness" to your feeling of enthusiasm, surprise, disappointment, etc.:
C'est bon ça, mon gars !
Ben mon vieux, t'as pas de chance !
j'adore ça, mec !
Mon ami, tu sais pas ce que tu rates !
man, was it big! / bon sang, qu'est-ce que c'était grand !